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In case where religious elderly parents live with their children who are not religious and do not keep Kosher, if needed for health, and lacking another alternative, if the parent sees on a constant basis that their children would never introduce non-Kosher to them in order to not cause them pain, then they can be lenient. However, someone healthy, or other people (someone not living in the house?), or someone who has alternatives (it is not a שעת הדחק) should be strict.

Could you please summarize his answer? Many (most?) of us don't read Hebrew, and it's always more convenient for answers to include the actual answer (even if only a summary) rather than just a link to it, even if it were in English.
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BrandonJul 27 '11 at 16:48